Analytical and numerical techniques will be applied to the study of host-parasite coevolution. In particular, the quasispecies model of Eigen can be manipulated to provide a non-linear set of equations that can describe a wide variety of interacting species. By choosing the parameters of the model, these equations can describe various forms of parasitism, symbiotic commensalism and mutualism. The inclusion of experimental data in these choices should allow for a reasonable description of numerous important parasites, such as Ebola and HIV. Numerically, a set of simulations will be implemented to study the effects of the fitness landscape on evolutionary dynamics. As well, these simulations can be used to gauge the validity of the approximations inherent in our analytical model. Together, these form a complementary set of methods that can shed light on a variety of topics, including population genetics, evolution, drug design and the nature of diseases.